Fixed points and boundary layers in exclusion processes

Abstract

In this paper, we show how a fixed point based boundary layer analysis can be used to understand phases and phase transitions in asymmetric simple exclusion processes (ASEPs) with open boundaries. In order to illustrate this method, we choose a two-species ASEP which has interesting phase transitions not seen in the one-species case. We also apply this method to the single species problem where the analysis is simple but nevertheless quite insightful.

5 pages, five figures; minor modifications, acknowledgement added

References in corpus (5)

• Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries
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• Duality and phase diagram of one dimensional transport
• Nonequilibrium tricriticality in one dimension

Cited by in corpus (11)

• Asymmetric coupling in two-lane simple exclusion process with Langmuir kinetics: phase diagrams and boundary layers
• Phase diagram of two-lane driven diffusive systems
• Multilane driven diffusive systems
• Phase-plane analysis of driven multi-lane exclusion models
• Phase coexistences and particle non-conservation in a closed asymmetric exclusion process with inhomogeneities
• Phase segregation and transport in a two species multi-lane system
• Steady states and phase transitions in heterogeneous asymmetric exclusion processes
• Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with particle nonconservation
• Coupling driven exclusion and diffusion processes on parallel lanes: boundary induced phase transitions and boundary layers
• Multi-shocks in asymmetric simple exclusions processes: Insights from fixed-point analysis of the boundary-layers
• Renormalization group analysis for an asymmetric simple exclusion process